Internal problem ID [2002]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.30 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (2 \sin \left (y\right )-x \right ) y^{\prime }-\tan \left (y\right )=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = \frac {\pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 6.969 (sec). Leaf size: 18
dsolve([(2*sin(y(x))-x)*diff(y(x),x)=tan(y(x)),y(0) = 1/2*Pi],y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\frac {x}{2}+\frac {\sqrt {x^{2}+4}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 17.52 (sec). Leaf size: 67
DSolve[{(2*Sin[y[x]]-x)*y'[x]==Tan[y[x]],y[0]==Pi/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cot ^{-1}\left (\sqrt {\frac {x^2}{2}-\frac {1}{2} \sqrt {x^4+4 x^2}}\right ) \\ y(x)\to \cot ^{-1}\left (\frac {\sqrt {x^2+\sqrt {x^2 \left (x^2+4\right )}}}{\sqrt {2}}\right ) \\ \end{align*}